Identification of real sinusoids in noise, the global matched filter approach.

Abstract

We consider the basic identification of real sinusoids in Gaussian noise problem. Since the maximum likelihood function is ill-conditioned and possesses numerous local maxima, we propose to somehow approximate it by a function that is convex and easy to optimize. The procedure amounts to apply the Global Matched Filter to the present problem using a complex redundant basis. It performs simultaneously the detection of the sinusoids and the identification of their characteristics. From a detection point of view, it is similar to a generalized likelihood ratio approach. The performances are close to the Cramer-Rao bounds for scenarios where few competing methods work. The approach can handle arbitrarily sampled data without further difficulties.